Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation

Details Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation Transport properties of heterogeneous materials derived from Gaussian random fields: Bounds and Simulation

2000-04-27

arxiv.org/abs/cond-mat/0004462v1

Phys. Rev. E Vol 51(5) pages 4141-4154 (1995)

Physics

Condensed Matter

Materials Science

15 pages, 14 figures

Scientific paper

10.1103/PhysRevE.51.4141

We investigate the effective conductivity ($\sigma_e$) of a class of amorphous media defined by the level-cut of a Gaussian random field. The three point solid-solid correlation function is derived and utilised in the evaluation of the Beran-Milton bounds. Simulations are used to calculate $\sigma_e$ for a variety of fields and volume fractions at several different conductivity contrasts. Relatively large differences in $\sigma_e$ are observed between the Gaussian media and the identical overlapping sphere model used previously as a `model' amorphous medium. In contrast $\sigma_e$ shows little variability between different Gaussian media.

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